homotopy representations and spheres of representations
Copyright policy )homotopy representations and spheres of representations
Let V(G) be the group of homotopy representations of the finite group G introduced by the reviewer and \textit{T. Petrie} [Publ. Math., Inst. Haut. Étud. Sci. 56, 129-170 (1982; Zbl 0507.57025)] and let V(G,l)\(\subset V(G)\) be the subgroup represented by linear representations. The author shows that \(V(G,l)=V(G)\) if and only if G is cyclic or a dihedral 2- group. A similar result is shown for the Picard group of the Burnside ring provided G is assumed nilpotent.
- Osaka University Japan
cyclic group, linear representations, Burnside ring, Finite transformation groups, 57S25, Picard group, dihedral 2-group, group of homotopy representations, 57S17, finite group actions
cyclic group, linear representations, Burnside ring, Finite transformation groups, 57S25, Picard group, dihedral 2-group, group of homotopy representations, 57S17, finite group actions
citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!